Convolution Lagrangian perturbation theory for biased tracers

Carlson, Jordan; Reid, Beth; White, Martin

doi:10.1093/mnras/sts457

Cited by 229 publications

(422 citation statements)

References 42 publications

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“…Therefore we will not use (A21) and instead calibrate the bias model following the procedure of [33,46] by treating the mass M appearing in (A20) as a free parameter and find the optimal mass M opt by fitting the TCLPT correlation function ξ X (r, M) with unspecified M to the HR2 real space correlation function. Once this optimal mass M opt is determined for each mass bin, the statistical averages ∂ n δ R F that also enter TCLPT expressions for v 12 (r), σ 2 ⊥ (r) and σ 2 || (r) will be identified with b n (M opt ) as suggested in [27,33,46]. Thus v 12 (r), σ 2 ⊥ (r) and σ 2 || (r) as well as the GSM redshift space correlation function ξ X (s) will then be determined without any further fits.…”

Section: Lagrangian Halo Density Field and Biasmentioning

confidence: 99%

“…Not however that there is no a priori reason that the bias coefficients in the expansion (A19), used in this work, are similar to those appearing in (A18) in the limit S 0 → 0. Therefore we won't use (A21) and instead will assist the bias model following the procedure of [33,46] by treating the mass M appearing in (A20) as a free parameter and find the optimal mass M opt by fitting the theoretical model to the real space correlation function. Following [27,33,46], we will identify those fitted bias parameters with the statistical average F (n) = b n (M opt ) as they arise in integrated Lagrangian perturbation theory [27] and convolution Lagrangian perturbation theory [33].…”

Section: B Local Lagrangian Bias Modelmentioning

confidence: 99%

“…Many more accurate models for connecting the dark matter field to halos in redshift space have been developed and their performance tested against Nbody simulations [26][27][28][29][30][31][32][33][34]. Here we focus on the Gaussian Streaming Model (GSM), [35][36][37], according to which one can approximate the redshift space halo correlation function by a convolution of the real space correlation and an approximately Gaussian velocity distribution whose mean and variance are given by the scale-dependent mean and dispersion of the pairwise velocity.…”

Section: Introductionmentioning

confidence: 99%

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Gaussian streaming with the truncated Zel’dovich approximation

2016

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We calculate the dark matter halo correlation function in redshift space using the Gaussian streaming model (GSM). To determine the scale dependent functions entering the streaming model we use local Lagrangian bias together with Convolution Lagrangian perturbation theory (CLPT) which constitutes an approximation to the Post-Zel'dovich approximation. On the basis of N-body simulations we demonstrate that a smoothing of the initial conditions with the Lagrangian radius improves the Zel'dovich approximation and its ability to predict the displacement field of proto-halos. Based on this observation we implement a "truncated" CLPT by smoothing the initial power spectrum and investigate the dependence of the streaming model ingredients on the smoothing scale. We find that the real space correlation functions of halos and their mean pairwise velocity are optimised if the coarse graining scale is chosen to be 1 Mpc/h at z = 0, while the pairwise velocity dispersion is optimised if the smoothing scale is chosen to be the Lagrangian size of the halo. We compare theoretical results for the halo correlation function in redshift space to measurements within the Horizon Run 2 N-body simulation halo catalog. We find that this simple two-filter smoothing procedure in the spirit of the truncated Zel'dovich approximation significantly improves the GSM+CLPT prediction of the redshift space halo correlation function over the whole mass range from large galaxy to galaxy cluster-sized halos.

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Section: Lagrangian Halo Density Field and Biasmentioning

confidence: 99%

Section: B Local Lagrangian Bias Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Gaussian streaming with the truncated Zel’dovich approximation

2016

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“…Accordingly, the truncated Post-Zel'dovich approximation (TPZA) with a smoothed initial power spectrum performs even better than TZA, compare [33,34]. We apply the framework of Convolution Lagrangian perturbation theory (CLPT) developed in [35] which recovers the ZA at lowest order while providing an approximation to PZA at higher order. CLPT can be understood as a partial resummation of the formalism presented in [36] providing a nonperturbative resummation of LPT that incorporates nonlinear halo bias.…”

Section: Introductionmentioning

confidence: 99%

Edgeworth streaming model for redshift space distortions

Uhlemann

Kopp

Haugg³

2015

Phys. Rev. D

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We derive the Edgeworth streaming model (ESM) for the redshift space correlation function starting from an arbitrary distribution function for biased tracers of dark matter by considering its two-point statistics and show that it reduces to the Gaussian streaming model (GSM) when neglecting non-Gaussianities. We test the accuracy of the GSM and ESM independent of perturbation theory using the Horizon Run 2 N-body halo catalog. While the monopole of the redshift space halo correlation function is well described by the GSM, higher multipoles improve upon including the leading order non-Gaussian correction in the ESM: the GSM quadrupole breaks down on scales below 30 Mpc/h whereas the ESM stays accurate to 2% within statistical errors down to 10 Mpc/h. To predict the scale dependent functions entering the streaming model we employ Convolution Lagrangian perturbation theory (CLPT) based on the dust model and local Lagrangian bias. Since dark matter halos carry an intrinsic length scale given by their Lagrangian radius, we extend CLPT to the coarsegrained dust model and consider two different smoothing approaches operating in Eulerian and Lagrangian space, respectively. The coarse-graining in Eulerian space features modified fluid dynamics different from dust while the coarse-graining in Lagrangian space is performed in the initial conditions with subsequent single streaming dust dynamics, implemented by smoothing the initial power spectrum in the spirit of the truncated Zel'dovich approximation. Finally, we compare the predictions of the different coarse-grained models for the streaming model ingredients to N-body measurements and comment on the proper choice of both the tracer distribution function and the smoothing scale. Since the perturbative methods we considered are not yet accurate enough on small scales, the GSM is sufficient when applied to perturbation theory.

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“…Nonlinearity in the power spectrum can be modeled using perturbation theory (PT) [19] and numerical simulations [20,21]. The nonlinearity of RSD was first modeled for dark matter [22][23][24][25][26][27][28][29][30], and the formalisms have been extended to dark matter halos [31][32][33][34][35][36][37][38][39]. Although detailed studies are required to fully understand halo bias [40][41][42][43], the theoretical models for the redshift-space power spectrum of halos were shown to work well up to reasonably small scales.…”

Section: Introductionmentioning

confidence: 99%

Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

Okumura

Hand²,

Seljak

et al. 2015

Phys. Rev. D

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Theoretical modeling of the redshift-space power spectrum of galaxies is crucially important to correctly extract cosmological information from galaxy redshift surveys. The task is complicated by the nonlinear biasing and redshift space distortion (RSD) effects, which change with halo mass, and by the wide distribution of halo masses and their occupations by galaxies. One of the main modeling challenges is the existence of satellite galaxies that have both radial distribution inside the halos and large virial velocities inside halos, a phenomenon known as the Finger-of-God (FoG) effect. We present a model for the redshift-space power spectrum of galaxies in which we decompose a given galaxy sample into central and satellite galaxies and relate different contributions to the power spectrum to 1-halo and 2-halo terms in a halo model. Our primary goal is to ensure that any parameters that we introduce have physically meaningful values, and are not just fitting parameters. For the lowest order 2-halo terms we use the previously developed RSD modeling of halos in the context of distribution function and perturbation theory approach. This term needs to be multiplied by the effect of radial distances and velocities of satellites inside the halo. To this one needs to add the 1-halo terms, which are non-perturbative. We show that the real space 1-halo terms can be modeled as almost constant, with the finite extent of the satellites inside the halo inducing a small k 2 R 2 term over the range of scales of interest, where R is related to the size of the halo given by its halo mass. We adopt a similar model for FoG in redshift space, ensuring that FoG velocity dispersion is related to the halo mass. For FoG k 2 type expansions do not work over the range of scales of interest and FoG resummation must be used instead. We test several simple damping functions to model the velocity dispersion FoG effect. Applying the formalism to mock galaxies modeled after the "CMASS" sample of the BOSS survey, we find that our predictions for the redshift-space power spectra are accurate up to k ≃ 0.4 h Mpc −1 within 1% if the halo power spectrum is measured using N -body simulations and within 3% if it is modeled using perturbation theory.

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Convolution Lagrangian perturbation theory for biased tracers

Cited by 229 publications

References 42 publications

Gaussian streaming with the truncated Zel’dovich approximation

Gaussian streaming with the truncated Zel’dovich approximation

Edgeworth streaming model for redshift space distortions

Galaxy power spectrum in redshift space: Combining perturbation theory with the halo model

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